Time Value of Money: The Foundation of Finance
The time value of money (TVM) says that a dollar today is worth more than a dollar in the future. It sits behind how companies evaluate projects, how bonds get priced, and why banks charge interest. This article covers the core TVM building blocks: future value, present value, and discount rates.
Key takeaway: You cannot compare cash flows at different points in time without adjusting for compounding or discounting first.
Why Is a Dollar Today Worth More?
There are three reasons a dollar today is worth more than a dollar tomorrow:
- Opportunity cost: Money received now can be invested to earn a return. A dollar today could grow to more than a dollar by next year.
- Inflation: Over time, prices tend to rise. The same dollar buys less in the future than it does today.
- Risk: A future payment is never guaranteed. The longer you wait, the greater the chance something goes wrong.
These factors mean that when comparing cash flows at different points in time, you cannot simply add them together. You need a way to express them in equivalent terms. That is what TVM calculations do.
Future Value
Future value (FV) answers the question: if I invest a certain amount today at a given rate, how much will it be worth in the future?
The formula is:
FV = PV x (1 + r)^n
- PV: Present value (the amount you start with)
- r: Interest rate per period (as a decimal)
- n: Number of periods
For example, if you invest $1,000 at 6% annual interest for 5 years:
FV = 1000 x (1.06)^5 = $1,338
Here is how the $1,000 grows year by year:
| Year | Starting Balance | Interest (6%) | Ending Balance |
|---|---|---|---|
| 1 | $1,000 | $60 | $1,060 |
| 2 | $1,060 | $64 | $1,124 |
| 3 | $1,124 | $67 | $1,191 |
| 4 | $1,191 | $71 | $1,262 |
| 5 | $1,262 | $76 | $1,338 |
The interest earned grows each year. In year 1 you earn $60, but by year 5 you earn $76. You earn interest on the original $1,000 and on the interest from prior years. That is compounding.
Present Value
Present value (PV) works in the opposite direction. It answers the question: what is a future cash flow worth in today's dollars?
The formula is:
PV = FV / (1 + r)^n
This process is called discounting. The rate used is known as the discount rate, and it reflects the required return or opportunity cost of capital.
For example, if someone promises to pay you $1,500 in 4 years and your required return is 8%:
PV = 1500 / (1.08)^4 = $1,103
This means you would be indifferent between receiving about $1,103 today and $1,500 four years from now, assuming an 8% return is available elsewhere.
To see how sensitive present value is to the discount rate, consider the same $1,500 payment in 4 years at different rates:
| Discount Rate | Calculation | Present Value |
|---|---|---|
| 4% | 1500 / (1.04)^4 | $1,282 |
| 6% | 1500 / (1.06)^4 | $1,188 |
| 8% | 1500 / (1.08)^4 | $1,103 |
| 10% | 1500 / (1.10)^4 | $1,025 |
| 12% | 1500 / (1.12)^4 | $953 |
The higher the discount rate, the less a future payment is worth today.
Discount Rate
Choosing the right discount rate depends on context:
- Corporate finance: Firms often use their weighted average cost of capital (WACC).
- Investment analysis: Analysts pick a required return based on the risk of the asset.
- Fixed income: Bond pricing uses the yield to maturity.
TVM with Multiple Cash Flows
Most financial decisions involve a series of cash flows, not just one payment. To find the total present value, you discount each cash flow and sum them:
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n
This is discounted cash flow (DCF) analysis. It lets you compare investments by bringing every future cash flow back to the present.
Why TVM Matters
TVM shows up across finance:
- Capital budgeting: Net present value (NPV) compares the present value of a project's cash inflows against its upfront cost.
- Bond pricing: A bond's price is the present value of its coupon payments and face value.
- Stock valuation: Dividend discount models and DCF models discount expected future cash flows.
- Loan amortization: Monthly payments are sized so that their present value equals the loan principal.
Every one of these starts with the same step: move cash flows to the same point in time before comparing them.
Conclusion
TVM connects present and future cash flows through compounding and discounting. Once you are comfortable with future value, present value, and how discount rates work, the rest of finance builds on top.
For a closer look at how PV and FV relate in practice, see our guide on present value vs. future value.
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